Simulation of statistical packings of spherical particles

An algorithm has been developed which simulates the process of statistically filling a fixed volume with spherical particles and which allows one to obtain the distributions of the coordination numbers of particles depending on the packing density.Institute of Engineering Chemistry, Ural Branch, Russian Academy of Sciences, Perm. Translated from Inzhenerno-Fizicheski Zhurnal, Vol. 63, No. 1, pp. 69–71, July, 1992.     

On the statistical nature of fracture

This paper explores the statistical nature of the mechanisms of fracture in structural materials and the loads that initiate them. The result of employing either a weak link or bundle model in the application of statistics to problems of fracture is examined. Experimental data is presented for the fracture of metal chains and the fracture of sheet aluminum containing machined cut-outs and cracks. The scatter in fracture loads for the chains and fracture toughness for the sheet specimens is statistically analyzed utilizing four statistical distributions: normal, lognormal, extreme value, and two-parameter Weibull functions. Based upon this work there appears to be no general a priori justification to utilize either the weak link or the bundle model in the statistical assessment of the fracture of typical engineering structural components.     

On the logical development of statistical models

Resumen This pager presents a classification of statistical models using a simple and logical framework. Some remarks are made about the historical appearance of each type of model and the practical problems that motivated them. It is argued that the current stages of the statistical methodology for model building have arisen in response to the needs of more sophisticated procedures for building dynamic-explicative types of models. Some potentially important topics for future research are included.     

Determination of the statistical characteristics of the chaotic motion of particles in a fluidized bed

A method of automation of the measurement of the effective diffusion coefficient in a fluidized bed is proposed and developed.     

On the statistical characteristics of fatigue crack propagation

In order to investigate the governing factor which causes the statistical fluctuation in the fatigue crack growth process, various experimental and simulated results obtained based on the Paris-Erdogan equation of fatigue crack growth rate were surveyed. Then, the governing factors for the randomness in microscopic fatigue fracture process being reflected on the phenomenological crack growth characteristics were examined. As a result, the distribution of the resisting strength of material to crack propagation with a certain unit size US is considered to be important. Also, the significance of the restriction of crack plane, that it can not rotate remarkably around the crack growth direction axis, is also indicated.     

On fatigue lifetimes and fatigue crack growth behavior of bone cement

Bone cement is used to develop a mechanical bond between an artificial joint and the adjacent bone tissue, and any degradation of this bond is of serious concern since it can lead to loosening and eventually malfunction of the artificial joint. In the present study, the fatigue lives and fatigue crack propagation behavior of two bone cements, CMW Type 3 and Zimmer, were investigated, and it was found that the size and distribution of pores played a major role in influencing both the fatigue crack initiation and propagation processes. The fatigue lifetimes of CMW exceeded those of Zimmer because of a lesser density of large pores. When the fatigue lifetimes were plotted as a function of K _limax, the maximum initial stress intensity factor based upon the initiating pore size, the difference in fatigue lifetimes between CMW and Zimmer bone cements was greatly reduced. The fatigue crack growth behavior of both bone cements were similar. This is a further indication that the noted differences in fatigue lifetimes were related to the size of the pore at the crack initiating site.     

The profound impact of negative power law noise on statistical estimation

This paper investigates the profound impact of negative power law (neg-p) noise-that is, noise with a power spectral density L_p(f) ? | f |^p for p < 0 - on the ability of practical implementations of statistical estimation or fitting techniques, such as a least squares fit (LSQF) or a Kalman filter, to generate valid results. It demonstrates that such neg-p noise behaves more like systematic error than conventional noise, because neg-p noise is highly correlated, non-stationary, non-mean ergodic, and has an infinite correlation time ?_c. It is further demonstrated that stationary but correlated noise will also cause invalid estimation behavior when the condition T ? ?_c is not met, where T is the data collection interval for estimation. Thus, it is shown that neg-p noise, with its infinite ?_c, can generate anomalous estimation results for all values of T, except in certain circumstances. A covariant theory is developed explaining much of this anomalous estimation behavior. However, simulations of the estimation behavior of neg-p noise demonstrate that the subject cannot be fully understood in terms of covariant theory or mean ergodicity. It is finally conjectured that one must investigate the variance ergodicity properties of neg-p noise through the use of 4th order correlation theory to fully explain such simulated behavior.     

On the oscillatory motion of aerosol particles

The oscillatory motion of moderately large, spherical, solid aerosol particles occurring in a binary gas mixture under the action of a periodic external force is considered. The system is described within the framework of a mathematical and physical approach developed by Landau and Fuks [1, 2] for a generalized problem considered with an allowance for the isothermal sliding. This effect arises when the medium features a mass-average velocity gradient. Estimates show that the influence of isothermal sliding on the character of oscillations of moderately large aerosol particles depends on the frequency and can reach up to 20% of the total velocity.     

On a statistical h index

The measurement of the quality of academic research is a rather controversial issue. Recently Hirsch has proposed a measure that has the advantage of summarizing in a single summary statistics the information that is contained in the citation counts of each scientist. From that seminal paper, a huge amount of research has been lavished, focusing on one hand on the development of correction factors to the h index and on the other hand, on the pros and cons of such measure proposing several possible alternatives. Although the h index has received a great deal of interest since its very beginning, only few papers have analyzed its statistical properties and implications. In the present work we propose a statistical approach to derive the distribution of the h index. To achieve this objective we work directly on the two basic components of the h index: the number of produced papers and the related citation counts vector, by introducing convolution models. Our proposal is applied to a database of homogeneous scientists made up of 131 full professors of statistics employed in Italian universities. The results show that while “sufficient” authors are reasonably well detected by a crude bibliometric approach, outstanding ones are underestimated, motivating the development of a statistical based h index. Our proposal offers such development and in particular confidence intervals to compare authors as well as quality control thresholds that can be used as target values.     

On statistical mechanics of vortex lines

An ensemble of a large number of vortex lines in cylindrical bounded domain is being considered. A system of equations determining the statistical characteristics of vortex line motion is derived from the assumption that this motion is ergodic and vortex lines are sufficiently smooth. The smoothness of vortex lines is characterized by vortex diffusivity. Both cases of finite and infinite vortex diffusivity are discussed. The continuum limit equations are obtained.     

On the subsample bootstrap variance estimation

In this paper we further elaborate on the subsample bootstrap result of Politis and Romano. Combining the jackknife and bootstrap ideas we were able to establish a wide consistency for the subsample bootstrap variance estimator. This was confirmed by simulations. Research partly supported by NSF Grant No. DMS-93-00725     

On the asymptotics of minimum disparity estimation

Inference procedures based on the minimization of divergences are popular statistical tools. Beran (Ann stat 5(3):445–463, 1977) proved consistency and asymptotic normality of the minimum Hellinger distance (MHD) estimator. This method was later extended to the large class of disparities in discrete models by Lindsay (Ann stat 22(2):1081–1114, 1994) who proved existence of a sequence of roots of the estimating equation which is consistent and asymptotically normal. However, the current literature does not provide a general asymptotic result about the minimizer of a generic disparity. In this paper, we prove, under very general conditions, an asymptotic representation of the minimum disparity estimator itself (and not just for a root of the estimating equation), thus generalizing the results of Beran (Ann stat 5(3):445–463, 1977) and Lindsay (Ann stat 22(2):1081–1114, 1994). This leads to a general framework for minimum disparity estimation encompassing both discrete and continuous models.     

A statistical model for the calculation of the frequency of turbulent collisions of particles of arbitrary density

A statistical model is given for determining the kernel of collisions of inertial particles (droplets, bubbles) in the entire range of variation of the density ratio between the dispersed and continuous phases. The model is based on the assumption that the joint probability density function of velocities of continuous medium and particles is a Gaussian distribution. The ranges of variation of bubble sizes are determined, in which the decisive part is played by the “inertial” and “spatial” collision mechanisms.     

On estimation of materials durability

A wear resistance function was proposed to characterize relative wear resistance of materials. Submitted results make it possible to determine parameters of the wear resistance or durability of materials and protective coatings. Franko Drogobych State Pedagogic Institute, Drogobych. Lublin Polytechnic Institute, Lublin, Poland. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 6, pp. 88–92, November–December, 1997.     

Preliminary estimation of parameters of beta distributions as statistical models of measurement series

Graph-analytic methods based on quantiles and moments are provided for preliminary estimation of parameters of beta-distributions as statistical models of measurement series. St. Petersburg, Shipbuilding Institute. Translated from Izmeritel'naya Tekhnika, No. 2, pp. 6–9, February, 1996.     

On the estimation of the expected number of accidents

We show that similar entities (drivers, intersections, bus companies, rail crossings) which in one period recorded "x" accidents do not have, on the average, "x" accidents in the subsequent period. The difference is large and systematic. This leads us to conclude that in circumstances in which only the safety estimates in these two periods matter, use of "x" to estimate the expected number of accidents has definite shortcomings. Better estimators are suggested, explored and their use is illustrated. We note that the suggested estimators are similar to what is used when estimation is based on a "treatment-control" type experimental design. It is hoped that the suggested estimators will alleviate some practical problems in the structuring of controlled experiments in safety research, eliminate bias-by-selection from uncontrolled studies and in general enhance the accuracy of safety estimates.     

On the estimation of the toughness of surface microcracks

Hardness testing is a method frequently used for evaluating the resistance of body surfaces to the influence of contact loading. The Vickers hardness test is applied for this purpose in a case when the material is sufficiently ductile and no cracks occur in the corners of the indents. Testing of the surface hardness of such materials as glass and ceramics on the basis of the Vickers testing method must take into account the energy that is spent on crack spreading. This paper describes a more exact and accurate method for evaluating resistance to microcrack formation on the surface of a material. To evaluate the conditions for crack spreading, it is necessary to test a specimen under loading in bulk. The suggested procedure involves a bent strip. As bending stresses are known, from the differences in crack length along and across the strip, the resistance of the material surface to crack propagation is determined.